High-gain observer with sliding mode for nonlinear state estimation and fault reconstruction

This paper develops a high gain observer with multiple sliding modes for simultaneous state and fault estimations for MIMO nonlinear systems. The novelty lies in the observer design that employs the combination of high-gain observer and sliding mode observer. The proposed observer does not impose the small-Lipschitz-constant condition on the system nonlinearity. By imposing a structural assumption on the nonlinear fault distribution matrix, the observability of the faults/unknown inputs w.r.t. the outputs is safeguarded and sliding modes are utilized for their reconstruction. The reconstruction of the faults from the sliding mode only relies on the output estimation error and thus can be implemented online together with the state estimation. Finally, an application to flexible joint robotic arm is used to illustrate the proposed method.     

Sampled-data control for time-delay systems

The sampled-data systems are hybrid ones involving continuous time and discrete time signals, which makes the traditional analysis and synthesis methodologies of time-delay systems unable to be directly used in the cases of hybrid systems with time-delay. The primary disadvantages of current design techniques of sampled-data control are their inabilities to deal effectively with time-delay and the model uncertainty. In this paper, we generalized the analysis methodology of time-delay systems to that of the hybrid systems with time-delay and uncertainty, which developed a design procedure of sampled-data control for time-delay systems. Asymptotic stability of the time-delay hybrid systems was developed. The time-delay dependent robust sampled-data control for the time-varying delay of an uncertain linear system was then discussed. The results were described as linear matrix inequalities, which can be solved using newly released LMITool.     

Rapid fault reconstruction using a bank of sliding mode observers

This paper deals with the design of a model-based rapid fault detection and isolation strategy using sliding mode observers. To address this problem, a new scheme is proposed by adaptively combining the information provided by a bank of observers. In this regard, a new structure for sliding mode observers is considered. Then, the well-known recursive least square algorithm is utilized to merge individual state estimations suitably such that the system fault is detected faster. The required condition for enhancing perfect state estimation is derived, and the stability of the overall system is proven via Lyapunov’s direct method. The supremacy of proposed scheme is fully discussed through mathematical analyses as well as simulations.     

Fault reconstruction using a LPV sliding mode observer for a class of LPV systems

This paper proposes a new sliding mode observer for fault reconstruction, applicable for a class of linear parameter varying (LPV) systems. Observer schemes for actuator and sensor fault reconstruction are presented. For the actuator fault reconstruction scheme, a virtual system comprising the system matrix and a fixed input distribution matrix is used for the design of the observer. The fixed input distribution matrix is instrumental in simplifying the synthesis procedure to create the observer gains to ensure a stable closed-loop reduced order sliding motion. The ‘output error injection signals’ from the observer are used as the basis for reconstructing the fault signals. For the sensor fault observer design, augmenting the LPV system with a filtered version of the faulty measurements allows the sensor fault reconstruction problem to be posed as an actuator fault reconstruction scenario. Simulation tests based on a high-fidelity nonlinear model of a transport aircraft have been used to demonstrate the proposed actuator and sensor FDI schemes. The simulation results show their efficacy.     

Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer

Over the last decade, considerable interest has been shown from industry, government and academia to the design of Vertical Take-Off and Landing (VTOL) autonomous aerial vehicles. This paper uses the recently developed sliding mode control driven by sliding mode disturbance observer (SMC-SMDO) approach to design a robust flight controller for a small quadrotor vehicle. This technique allows for a continuous control robust to external disturbance and model uncertainties to be computed without the use of high control gain or extensive computational power. The robustness of the control to unknown external disturbances also leads to a reduction of the design cost as less pre-flight analyses are required. The multiple-loop, multiple time-scale SMC-SMDO flight controller is designed to provide robust position and attitude control of the vehicle while relying only on knowledge of the limits of the disturbances. Extensive simulations of a 6 DOF computer model demonstrate the robustness of the control when faced with external disturbances (including wind, collision and actuator failure) as well as model uncertainties.     

Fixed-time nonlinear homogeneous sliding mode approach for robust tracking control of multirotor aircraft: Experimental validation

This paper presents a robust scheme for fixed-time tracking control of a multirotor system. The aircraft is subjected to matched lumped disturbances, i.e., unmodeled dynamics, parameters uncertainties, and external perturbations besides measurement noise. Firstly, a novel Nonlinear Homogeneous Continuous Terminal Sliding Manifold (NHCTSM) based on the weighted homogeneity theory is presented. The sliding manifold is designed with prescribed dynamics featuring Global Asymptotic Stability (GAS) and fixed-time convergence. Then, a novel Fixed-time Non-switching Homogeneous Nonsingular Terminal Sliding Mode Control (FNHNTSMC) is proposed for the position and attitude loops by employing the developed NHCTSM and an appropriate reaching law. Moreover, the control framework incorporates a disturbance observer to feedforward and compensate for the disturbances. The designed control scheme can drive the states of the system to the desired references in fixed-time irrespective of the values of the Initial Conditions (ICs). Since the existing works on homogeneous controllers rely on the bi-limit homogeneity concept in the convergence proofs, the estimate of the settling-time or its upper-bound cannot be given explicitly. In contrast, this study employs Lyapunov Quadratic Function (LQF) and Algebraic Lyapunov Equation (ALE) in the stability analysis of both controller and observer. Following this method, an expression of the upper-bound of the settling-time is explicitly derived. Furthermore, to assure the Uniform Ultimate Boundedness (UUB) of all signals in the feedback system, the dynamics of the observer and controller are jointly analyzed. Simulations and experiments are conducted to quantify the control performance. The proposed approach achieves superior performance compared with recent literature on fixed-time/finite-time control and a commercially available PID controller. The comparative results witness that the developed control scheme improves the convergence-time, accuracy, and robustness while overcoming the singularity issue and mitigating the chattering effect of conventional SMC.     

Hybrid sliding mode observer for switched linear systems with unknown inputs

This paper addresses the state observation and unknown input estimation of a class of switched linear systems with unknown inputs. This class of systems may have modes in which the state is not fully observable. A state transformation allows implementing two suitable reduced-order observers. The first one, based on second order sliding mode techniques, is proposed to reconstruct the discrete state in the presence of unknown inputs. The second one, based on gathering partial information from individual modes of the switched system and on higher order sliding mode techniques, is introduced to estimate the continuous state. Then, the observer injection signal of the first second order sliding mode observer is used to estimate the unknown inputs. Simulation results highlight the efficiency of the proposed method.     

Parameters estimation using sliding mode observer with shift operator

In different areas of engineering, mathematical models are used to describe real life phenomena and experiments are conducted to validate them. It is common that these models may contain a number of parameters that cannot be measured directly or calculated. Thus, parameter estimation is an important step in the process of modeling based on empirical data of the system.In the control system’s literature, one can find considerable amount of research in the area of system parameters identification. Most of these techniques are based on minimizing the estimation error in some statistical framework such as least square error based methods. In most cases, using these techniques, one can prove the uniform exponential stability of the state and parameter estimation error, but the convergence rate can be too low. However, when designing control systems, knowledge of unknown immeasurable (or even time varying) parameters might be crucial for the operation of the controller and thus have to be accurately estimated with a desired rate of convergence. In this paper, we demonstrate a way to provide an estimation technique with tunable convergence rate using sliding mode with linear operators such as time delay.     

Discrete time second order sliding mode observer for uncertain linear multi-output system

This paper presents a second order sliding mode observer (SOSMO) design for discrete time uncertain linear multi-output system. The design procedure is effective for both matched and unmatched bounded uncertainties and/or disturbances. A second order sliding function and corresponding sliding manifold for discrete time system are defined similar to the lines of continuous time counterpart. A boundary layer concept is employed to avoid switching across the defined sliding manifold and the sliding trajectory is confined to a boundary layer once it converges to it. The condition for existence of convergent quasi-sliding mode (QSM) is derived. The observer estimation errors satisfying given stability conditions converge to an ultimate finite bound (within the specified boundary layer) with thickness O(T²)$O\left(T^2\right)$ where T is the sampling period. A relation between sliding mode gain and boundary layer is established for the existence of second order discrete sliding motion. The design strategy is very simple to apply and is demonstrated for three examples with different class of disturbances (matched and unmatched) to show the effectiveness of the design. Simulation results to show the robustness with respect to the measurement noise are given for SOSMO and the performance is compared with pseudo-linear Kalman filter (PLKF).     

Impulsive fixed-time observer for linear time-delay systems

This paper presents a fixed-time observer for a general class of linear time-delay systems. In contrast to many existing observers, which normally estimate system’s trajectory in an asymptotic fashion, the proposed observer estimates system’s state in a prescribed time. The proposed fixed-time observer is realized by updating the observer in an impulsive manner. Simulation results are also presented to illustrate the convergence behavior of the proposed fixed-time observer.     

Design of adaptive sliding mode controller for robust tracking and model following

The problem of the robust tracking and model following for a class of linear systems with time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance is investigated in this paper. The algorithm is based on the adaptive sliding mode control. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. This scheme guarantees the closed-loop system stability and zero-tracking error in the presence of time-varying parameter uncertainties, multiple delayed state perturbations and external disturbance. Finally, simulation results demonstrate the efficacy of the proposed control methodology.     

Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection

Aiming at early detection of faults in dynamic systems subject to external periodic disturbances, this paper proposes a new generalized proportional-integral observer (GPIO) fault detection scheme with zero-pole joint optimization and novel complex coefficient gain (CCG) of residual evaluation. The focus of the proposed scheme is to reduce the adverse impacts caused by the semi-stationary periodic disturbance whose spectrum is uneven, with most energy being at some dominant frequencies. The proposed GPIO with a complex coefficient gain is designed in a two-stage procedure. In the first stage of zero assignment and pole optimization, the additional zeros introduced by the GPIO’s integration action are allocated to near the disturbance frequency. The gain of the transfer function matrix relating from the disturbances to the fault indicator signals is minimized by pole optimization. In the second stage of designing complex coefficient gain in residual evaluation, the unique feature of rank-deficient caused by the additional zeros assigned in stage one is further exploited to cancel the disturbances in the fault indicator signals (which is also referred to as the fault detection residual in this article). It is proved that, for an arbitrary periodic disturbance with a specific spectrum, the remnant components of the disturbance in the indicator signals generated by the GPIO can cancel each other by a complex gain vector, which can be determined by the zero eigenvalue’s left eigenvector of the rank-deficient of the disturbance transfer function matrix. The sufficient conditions for the convergence of the proposed fault detection filter are also given. Numerical examples illustrate the proposed method’s better performance in detecting minor faults.     

Dissipative state observer design for nonlinear time-delay systems

This paper is concerned with the design of dissipative state observers for a family of time-delay nonlinear systems. The Dissipativity method, proposed by one of the authors for delay-free nonlinear systems, is extended here to a class of time-delay nonlinear systems. The design method consists in decomposing the time-delay estimation error dynamics into a time-delay linear subsystem and a time-varying memoryless nonlinearity, connected in a negative feedback loop. By using some storage functionals, both delay-independent and delay-dependent dissipativity criteria are derived in order to guarantee the exponential convergence property of the observer. The exponential stability of the estimation error is then ensured, assuming that the nonlinearity is dissipative with respect to a quadratic supply rate and the linear part is designed, through the observer gains, to be dissipative with respect to a complementary supply rate. The design conditions are formulated in terms of tractable bilinear (BMI’s) or linear matrix inequalities (LMI’s). An interesting advantage is that the proposed dissipative design extends and generalizes under a unified framework several methods available in the literature, since a wide diversity of nonlinearities can be considered. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.     

Fractional-order sliding mode control for a bearingless induction motor based on improved load torque observer

In order to improve the anti-disturbance performance of a bearingless induction motor (BIM) control system, a fractional-order sliding mode control (FOSMC) strategy based on improved load torque observer is proposed on the basis of the sliding mode speed regulation system. Using the information memory and genetic characteristics of the fractional calculus operator, the fractional integral term of the speed error is introduced in the design of the traditional sliding surface, which reduces the influence of disturbance on the speed regulation system. The fractional-order sliding mode control law is derived based on the BIM mathematical model, and the stability of the control law is proved by Lyapunov theorem. An improved observer is constructed based on the BIM state equations, and the real-time observed load torque is introduced into the fractional-order sliding mode controller. To improve the observer's convergence speed, the proportional integral form is used to replace the integral form in the traditional reduced order load observer. And the state error feedback coefficients of the improved load observer are calculated. Both simulation and experimental results verified the effectiveness of the proposed control strategy.     

On robust stabilization of uncertain stochastic time-delay systems—an LMI-based approach

In this paper, we first deal with the robust stability of uncertain linear stochastic differential delay systems. The parameter uncertainties are time-varying and unknown but are norm-bounded via two types of uncertainties, and the delays are time invariant. We then extend the proposed theory to discuss the robust stabilization of uncertain stochastic differential delay systems. These results are given in terms of linear matrix inequalities. Two examples are presented to illustrate the effectiveness.     

A fast terminal sliding mode control scheme with time-varying sliding mode surfaces

This paper proposes a novel fast terminal sliding mode (FTSM) control scheme, which accelerates convergence of the controlled system both in its approaching and after reaching the sliding manifold. The novelty lies in the design of time-varying sliding surface without a priori knowledge of the initial system states, so achieving insensitivity to the uncertainty of the initial states. Based on this, we design a corresponding FTSM control strategy, where the singularity problem of conventional terminal sliding mode (TSM) control systems is overcome by restricting the TSM surfaces to non-singular areas. We prove stability and finite-time convergence of the system with the proposed controller. Furthermore, we extend the proposed FTSM control scheme to high-order systems and discuss its application in practical systems. Preliminary simulation results and comparative studies demonstrate the validity of the proposed FTSM control scheme with the designed sliding surface.     

Active fault tolerant control design for reusable launch vehicle using adaptive sliding mode technique

In this paper, the problem of active fault tolerant control for a reusable launch vehicle (RLV) with actuator fault using both adaptive and sliding mode techniques is investigated. Firstly, the kinematic equations and dynamic equations of RLV are given, which represent the characteristics of RLV in reentry flight phase. For the dynamic model of RLV in faulty case, a fault detection scheme is proposed by designing a nonlinear fault detection observer. Then, an active fault tolerant tracking strategy for RLV attitude control systems is presented by making use of both adaptive control and sliding mode control techniques, which can guarantee the asymptotic output tracking of the closed-loop attitude control systems in spite of actuator fault. Finally, simulation results are given to demonstrate the effectiveness of the developed fault tolerant control scheme.     

Observer-based terminal sliding mode control of non-affine nonlinear systems: Finite-time approach

This paper studies the problem of observer based fast nonsingular terminal sliding mode control schemes for nonlinear non-affine systems with actuator faults, unknown states, and external disturbances. A hyperbolic tangent function based extended state observer is considered to estimate unknown states, which enhances robustness by estimating external disturbance. Then, Taylor series expansion is employed for the non-affine nonlinear system with actuator faults, which transforms it to an affine form system to simplify disturbance observer and controller design. A finite time disturbance observer is designed to address unknown compound disturbances, which includes external disturbances and system uncertainties. A fast nonsingular terminal sliding mode with exponential function sliding mode is proposed to address output tracking. Simulation results show the proposed scheme is effective.     

Precise robust motion tracking of a piezoactuated micropuncture mechanism with sliding mode control

This paper proposes a novel model-based control scheme to achieve the precise robust motion control of a piezoactuated micropuncture mechanism for cell injection. Using the Bouc–Wen model, the hysteretic dynamic model of the micropuncture mechanism is constructed, and its local optimization is conducted to facilitate engineering applications. On the basis of this model, a controller that synthesizes a fast nonsingular terminal sliding mode (FNTSM) control and time-delay estimation (TDE) is constructed. The control law for FNTSM has the advantages of continuous output, absence of chatter, and finite-time convergence of tracking error. The unknown quantity for TDE technology can be estimated and compensated online to reduce the FNTSM gain. Experiments on the micropuncture mechanism demonstrate that the developed control scheme provides smaller tracking error than the delay-control strategy based on the linear-error dynamic model or the model-free control scheme (e.g., Jin and Hsia’s controller). Micropuncture experiments on zebrafish embryo are successfully completed. Moreover, from the practical aspects, the control scheme developed herein can be effectively implemented in other types of micro-operation mechanisms driven by piezoelectric actuators.     

A new singular system approach to output feedback sliding mode control for fractional order nonlinear systems

This paper studies the problem of output feedback sliding mode control (OFSMC) for fractional order nonlinear systems. A necessary and sufficient condition for the existence of a sliding surface is obtained by a new singular system approach and a linear matrix equality (LMI), which reduces the conservativeness of the system. Then an OFSMC law is designed based on a fractional order Lyapunov method, which ensures that the resulting fractional closed-loop system is asymptotically stable and the states of the fractional closed-loop system converge to the sliding surface in finite time. A fractional electrical circuit is discussed to illustrate the effectiveness of the proposed approach.